PHYSICAL REVIEW LETTERS PRL 107, 211801 (2011) week ending 18 NOVEMBER 2011 Determination of fs =fd for TeV pp Collisions and Measurement of the B0 ! D Kỵ Branching Fraction R Aaij et al.* (LHCb Collaboration) (Received 28 June 2011; published 14 November 2011) ỵ The relative abundance of the three decay modes B0 ! D K ỵ , B0 ! D ỵ , and B0s ! D s produced in TeV pp collisions at the LHC is determined from data corresponding to an integrated luminosity of 35 pbÀ1 The branching fraction of B0 ! DÀ K ỵ is found to be BB0 ! D K ỵ ị ẳ 2:01 ặ 0:18stat ặ 0:14syst ị 10À4 The ratio of fragmentation fractions fs =fd is determined through the relative ỵ to B0 ! D K þ and B0 ! DÀ þ , leading to f =f ẳ 0:253 ặ 0:017 ặ abundance of B0s ! DÀ s s d 0:017 Ỉ 0:020, where the uncertainties are statistical, systematic, and theoretical, respectively DOI: 10.1103/PhysRevLett.107.211801 PACS numbers: 13.25.Hw, 12.38.Qk, 13.60.Le, 13.87.Fh Knowledge of the production rate of B0s mesons is required to determine any B0s branching fraction This rate is determined by the bb" production cross section and the fragmentation probability fs , which is the fraction of B0s mesons among all weakly decaying bottom hadrons Similarly, the production rate of B0 mesons is driven by the fragmentation probability fd The measurement of the branching fraction of the rare decay B0s ! ỵ is a prime example where improved knowledge of fs =fd is needed to reach the highest sensitivity in the search for physics beyond the standard model [1] The ratio fs =fd is, in principle, dependent on collision energy and type as well as the acceptance region of the detector This is the first measurement of this quantity at the LHC The ratio fs =fd can be extracted if the ratio of branching fractions of B0 and B0s mesons decaying to particular final states X1 and X2 , respectively, is known: NX BðB0 ! X1 Þ ðB0 ! X1 Þ fs : ¼ fd NX1 BðB0s ! X2 Þ ðB0s ! X2 ị (1) ỵ The ratio of the branching fraction of the B0s ! DÀ s and À þ B ! D K decays is dominated by contributions from color-allowed tree-diagram amplitudes and is therefore theoretically well understood In contrast, the ratio of the ỵ branching ratios of the two decays B0s ! DÀ s and B ! ỵ D can be measured with a smaller statistical uncertainty due to the greater yield of the B0 mode but suffers from an additional theoretical uncertainty due to the contribution from a W-exchange diagram Both ratios are exploited here to measure fs =fd according to the equations [2,3] *Full author list given at the end of the article Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI 0031-9007=11=107(21)=211801(8) 2 f 2 fs D Kỵ NDs ỵ Bd Vus K ¼ 0:971 Vud f Bs N a N F Ds ỵ ND Kỵ fd (2) and B fs D ỵ NDs ỵ ẳ 0:982 d : fd Bs N a N F N E Ds ỵ ND ỵ (3) Here X is the selection efficiency of decay X (including the branching fraction of the D decay mode used to reconstruct it), NX is the observed number of decays of this type, the Vij are elements of the Cabibbo-KobayashiMaskawa matrix, fi are the meson decay constants, and the numerical factors take into account the phase space difference for the ratio of the two decay modes Inclusion of charge conjugate modes is implied throughout The term N a parametrizes nonfactorizable SUð3Þ-breaking effects; N F is the ratio of the form factors; N E is an additional correction term to account for the W-exchange diagram in the B0 ! D ỵ decay Their values [2,3] are N a ẳ 1:00 ặ 0:02, N F ẳ 1:24 Æ 0:08, and N E ¼ 0:966 Æ 0:075 The latest world average [4] is used for the B meson lifetime ratio Bs = Bd ẳ 0:973 ặ 0:015 The numerical values used for the other factors are jVus j ¼ 0:2252, jVud j ¼ 0:974 25, f ¼ 130:41, and fK ¼ 156:1, with negligible associated uncertainties [5] The observed yields of these three decay modes in 35 pbÀ1 of data collected with the LHCb detector in the 2010 running period are used to measure fs =fd averaged over the LHCb acceptance and to improve the current measurement of the branching fraction of the B0 ! D Kỵ decay mode [6] The LHCb experiment [7] is a single-arm spectrometer, designed to study B decays at the LHC, with a pseudorapidity acceptance of < < for charged tracks The first trigger level allows the selection of events with B hadronic decays using the transverse energy of hadrons measured in the calorimeter system The event information 211801-1 Ó 2011 CERN, for the LHCb Collaboration PRL 107, 211801 (2011) PHYSICAL REVIEW LETTERS is subsequently sent to a software trigger, implemented in a dedicated processor farm, which performs a final online selection of events for later offline analysis The tracking system determines the momenta of B decay products with a precision of p=p ¼ 0:35%–0:5% Two ring imaging Cherenkov detectors allow charged kaons and pions to be distinguished in the momentum range 2–100 GeV=c [8] The three decay modes B0 ! D Kỵ ịỵ , B0 ! ỵ ỵ D Kỵ ịKỵ , and B0s ! DÀ s ðK K Þ are topologically identical and can therefore be selected by using identical geometric and kinematic criteria, thus minimizing efficiency differences between them Events are selected at the first trigger stage by requiring a hadron with transverse energy greater than 3.6 GeV in the calorimeter The second, software, stage [9,10] requires a two-, three-, or four-track secondary vertex with a high sum pT of the tracks, significant displacement from the primary interaction, and at least one track with exceptionally high pT , large displacement from the primary interaction, and small fit 2 The decays of B mesons can be distinguished from the background by using variables such as the pT and impact parameter 2 of the B, D, and the final state particles with respect to the primary interaction In addition, the vertex quality of the B and D candidates, the B lifetime, and the angle between the B momentum vector and the vector joining the B production and decay vertices are used in the selection The D lifetime and flight distance are not used in the selection because the lifetimes of the DÀ s and DÀ differ by about a factor of The event sample is first selected by using the gradient boosted decision tree technique [11], which combines the geometrical and kinematic variables listed above The selection is trained on a mixture of simulated B0 ! D ỵ decays and combinatorial background selected from the sidebands of the data mass distributions The distributions of the input variables for data and simulated signal events show excellent agreement, justifying the use of simulated events in the training procedure Subsequently, DÀ (DÀ s ) candidates are identified by requiring the invariant mass under the K (KK) hypothesis to fall within the selection window 1870ỵ24 40 1969ỵ24 40 ị MeV=c , where the mass resolution is approximately 10 MeV=c2 The final B0 ! D ỵ and B0s ! ỵ D s subsamples consist of events that pass a particle identification (PID) criterion on the bachelor particle, based on the difference in log-likelihood between the charged pion and kaon hypotheses (DLL) of DLLðK À Þ < 0, with an efficiency of 83.0% The B0 ! D Kỵ subsample consists of events with DLLðK À Þ > 5, with an efficiency of 70.2% Events not satisfying either condition are not used The relative efficiency of the selection procedure is evaluated for all decay modes using simulated events, where the appropriate resonances in the charm decays are week ending 18 NOVEMBER 2011 taken into account As the analysis is sensitive only to relative efficiencies, the impact of differences between the data and simulation is small The relative efficiencies are D ỵ =D Kỵ ẳ 1:221 ặ 0:021, D Kỵ =Ds ỵ ẳ 0:917 ặ 0:020, and D ỵ =Ds ỵ ẳ 1:120 ặ 0:025, where the errors are due to the limited size of the simulated event samples The relative yields of the three decay modes are extracted from unbinned extended maximum likelihood fits to the mass distributions shown in Fig The signal mass shape is described by an empirical model derived from simulated events The mass distribution in the simulation exhibits non-Gaussian tails on either side of the signal The tail on the right-hand side is due to non-Gaussian detector effects and modeled with a crystal ball function [12] A similar tail is present on the left-hand side of the peak In addition, the low mass tail contains a second contribution due to events where hadrons have radiated photons that are not reconstructed The sum of these contributions is modeled with a second crystal ball function The peak values of these two crystal ball functions are constrained to be identical Various backgrounds have to be considered, in particular, the cross feed between the DÀ and DÀ s channels, and À the contamination in both samples from b ! ỵ c ỵ ỵ decays, where c ! pK The Ds contamination in the DÀ data sample is reduced by loose PID requirements, DLLðK À Þ < 10 (with an efficiency of 98.6%) and DLLðK À Þ > (with an efficiency of 95.6%), for the pions and kaons from D decays, respectively The resulting ỵ as background is efficiency to reconstruct B0s ! DÀ s evaluated, by using simulated events, to be 30 times smaller than for B0 ! D ỵ and 150 times smaller than for B0 ! D K ỵ within the B0 and D signal mass windows By taking into account the lower production fraction of B0s mesons, this background is negligible The contamination from Ãc decays is estimated in a similar way However, different approaches are used for the B0 and B0s decays A contamination of approximately 2% under the B0 ! DÀ ỵ mass peak and below 1% under the B0 ! D Kỵ peak is found, and therefore no explicit DLLp À Þ criterion is needed The Ãc background in the B0s sample is, on the other hand, large enough that it can be fitted for directly A prominent peaking background to B0 ! D Kỵ is B ! D ỵ , with the pion misidentified as a kaon The small ! K misidentification rate (of about 4%) is compensated by the larger branching fraction, resulting in similar event yields This background is modeled by obtaining a clean B0 ! D ỵ sample from the data and reconstructing it under the B0 ! D K ỵ mass hypothesis The resulting mass shape depends on the momentum distribution of the bachelor particle The momentum distribution after the DLLðK À Þ > requirement can be found by considering the PID performance as a function of 211801-2 PHYSICAL REVIEW LETTERS PRL 107, 211801 (2011) momentum This is obtained by using a sample of Dỵ ! D0 ỵ decays and is illustrated in Fig The mass distribution is reweighted by using this momentum distribution to reproduce the B0 ! D ỵ mass shape following the DLL cut The combinatorial background consists of events with random pions and kaons, forming a fake DÀ or DÀ s candidate, as well as real DÀ or DÀ mesons that combine with a s random pion or kaon The combinatorial background is modeled with an exponential shape Other background components originate from partially reconstructed B0 and B0s decays In B0 ! D ỵ , these originate from B0 ! D ỵ and B0 ! D ỵ decays, which can also be backgrounds for B0 ! DÀ Kỵ in the case of a misidentified bachelor pion In B0 ! D Kỵ , there is additionally background from B0 ! D Kỵ decays The invariant mass distributions for the partially reconstructed and misidentified backgrounds are taken from large samples of simulated events, reweighted according to the mass hypothesis of the signal being fitted and the DLL cuts ỵ ỵ For B0s ! D s , the B ! D background peaks under the signal with a similar shape In order to suppress this peaking background, PID requirements are placed on both kaon tracks The kaon which has the same sign in the ỵ ỵ B0s ! D s and B ! D decays is required to satisfy DLLðK À Þ > 0, while the other kaon in the Dỵ s decay is required to satisfy DLLðK À Þ > Because of the similar shape, a Gaussian constraint is applied to the yield of this background The central value of this constraint is computed from the ! K misidentification rate The b ! ỵ background shape is obtained from c simulated events, reweighted according to the PID efficiency, and the yield allowed to float in the fit Finally, ỵ ỵ the relative size of the B0s ! DÀ and B0s ! DÃÀ s s backgrounds is constrained to the ratio of the week ending 18 NOVEMBER 2011 B0 ! D ỵ and B0 ! D ỵ backgrounds in the B0 ! D ỵ fit, with an uncertainty of 20% to account for potential SUð3Þ symmetry breaking effects The free parameters in the likelihood fits to the mass distributions are the event yields for the different event types, i.e., the combinatorial background, partially reconstructed background, misidentified contributions, and the signal, as well as the peak value of the signal shape In addition, the combinatoric background shape is left free in ỵ fits, and the signal the B0 ! D ỵ and B0s ! D s ỵ width is left free in the B ! D fit In the B0s ! ỵ ỵ D s and B ! D K fits, the signal width is fixed to the value from the B0 ! D ỵ fit, corrected by the ratio of the signal widths for these modes in simulated events 0.8 Efficiency K→ K, DLL(K-π)>5 0.6 π →π , DLL(K-π)5 0.2 K→ π, DLL(K-π) or DLLðK À Þ < 0, respectively The correspondent probability to wrongly identify (open symbols) a pion as a kaon, or a kaon as a pion, is also shown The data are taken from a calibration sample of DÃ ! DðKÞ decays; the statistical uncertainties are too small to display FIG Mass distributions of the B0 ! D ỵ , B0 ! D K þ , þ candidates (top to bottom) The indicated and B0s ! DÀ s components are described in the text 211801-3 PRL 107, 211801 (2011) The fits to the full B0 ! D ỵ , B0 ! D Kỵ , and ỵ ! D s data samples are shown in Fig The result0 ing B ! DÀ ỵ and B0 ! D K ỵ event yields are 4103 Ỉ 75 and 252 Ỉ 21, respectively The number of misidentified B0 ! D ỵ events under the B0 ! D Kỵ signal as obtained from the fit is 131 Ỉ 19 This agrees with the number expected from the total number of B0 ! D ỵ events, corrected for the misidentification rate determined from the PID calibration sample, of 145 ặ The ỵ B0s ! D s event yield is 670 Ỉ 34 The stability of the fit results has been investigated by using different cut values for both the PID requirement on the bachelor particle and for the multivariate selection variable In all cases, variations are found to be small in comparison to the statistical uncertainty The relative branching fractions are obtained by correcting the event yields by the corresponding efficiency factors; the dominant correction comes from the PID efficiency The dominant source of systematic uncertainty is the knowledge of the B0 ! D ỵ branching fraction (for the B0 ! D Kỵ branching fraction measurement) and the knowledge of the DÀ and DÀ s branching fractions (for the fs =fd measurement) An important source of systematic uncertainty is the knowledge of the PID efficiency as a function of momentum, which is needed to reweight the mass distribution of the B0 ! D ỵ decay under the kaon hypothesis for the bachelor track This enters in two ways: first as an uncertainty on the correction factors and second as part of the systematic uncertainty, since the shape for the misidentified backgrounds relies on correct knowledge of the PID efficiency as a function of momentum The performance of the PID calibration is evaluated by applying the same method from the data to simulated events, and the maximum discrepancy found between the calibration method and the true misidentification is attributed as a systematic uncertainty The fs =fd measurement ỵ using B0 ! D Kỵ and B0s ! DÀ is more robust s against PID uncertainties, since the final states have the same number of kaons and pions Other systematic uncertainties are due to limited simulated event samples (affecting the relative selection effi ỵ ciencies), neglecting the b ! ỵ c and Bs ! Ds ỵ backgrounds in the B ! D fits, and the limited accuracy of the trigger simulation Even though the ratio of efficiencies is statistically consistent with unity, the maximum deviation is conservatively assigned as a systematic uncertainty The difference in interaction probability between kaons and pions is estimated by using Monte Carlo simulation The systematic uncertainty due to possible discrepancies between the data and simulation is expected to be negligible, and it is not taken into account The efficiency of the nonresonant Ds decays varies across the Dalitz plane but has a negligible effect on the total B0s ! ỵ D s efficiency The sources of systematic uncertainty are summarized in Table I B0s week ending 18 NOVEMBER 2011 PHYSICAL REVIEW LETTERS TABLE I Experimental systematic uncertainties for the BB0 ! D K ỵ Þ and the two fs =fd measurements PID calibration Fit model Trigger simulation BB0 ! D ỵ ị ỵ þ BðDþ s !K K Þ BðDþ ! K ỵ ỵ ị Bs = Bd BB0 ! D K þ Þ fs =fd 2.5% 2.8% 2.0% 4.9% 1:0%=2:5% 2.8% 2.0% 4.9% 2.2% 1.5% The efficiency corrected ratio of B0 ! D ỵ and B0 ! yields is combined with the world average of the B0 ! D ỵ [5] branching ratio to give D Kỵ B B0 ! D Kỵ ị ẳ 2:01 ặ 0:18 ặ 0:14ị 104 : (4) The first uncertainty is statistical and the second systematic The theoretically cleaner measurement of fs =fd uses ỵ B0 ! D Kỵ and B0s ! D s and is made according to Eq (2) By accounting for the exclusive D branching fractions BDỵ ! K ỵ ỵ ị ẳ 9:14 ặ 0:20ị% [13] ỵ ỵ and BDỵ s ! K K ị ẳ 5:50 ặ 0:27Þ% [14], the value of fs =fd is found to be fs =fd ẳ 0:310 ặ 0:030stat ặ 0:021syst ị ; N aN F (5) where the first uncertainty is statistical and the second is systematic The statistical uncertainty is dominated by the yield of the B0 ! DÀ Kỵ mode The statistically more precise but theoretically less clean measurement of fs =fd uses B0 ! D ỵ and B0s ! ỵ D s and is, from Eq (3), fs =fd ẳ 0:307 ặ 0:017stat ặ 0:023syst Þ : N aN FN E (6) The two values for fs =fd can be combined into a single value, taking all correlated uncertainties into account and using the theoretical inputs accounting for the SUð3Þ breaking part of the form factor ratio, the nonfactorizable and W-exchange diagram: fs =fd ¼ 0:253 Ỉ 0:017stat Ỉ 0:017syst Ỉ 0:020theor : (7) In summary, with 35 pbÀ1 of data collected by using the LHCb detector during the 2010 LHC operation at a centerof-mass energy of TeV, the branching fraction of the Cabibbo-suppressed B0 decay mode B0 ! D Kỵ has been measured with better precision than the current world average Additionally, two measurements of the fs =fd production fraction are performed from the relative yields ỵ ỵ of B0s ! DÀ and B0 ! s with respect to B ! D K ỵ D These values of fs =fd are numerically close to the values determined at LEP and at the Tevatron [4] 211801-4 PRL 107, 211801 (2011) PHYSICAL REVIEW LETTERS We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC We thank the technical and administrative staff at CERN and at the LHCb institutes and acknowledge support from the National Agencies: CAPES, CNPq, FAPERJ, and FINEP (Brazil); CERN; NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF, and MPG (Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR (Poland); ANCS (Romania); MinES of Russia and Rosatom (Russia); MICINN, Xuntagal, and GENCAT (Spain); SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA) We also acknowledge the support received from the ERC under FP7 and the Re´gion Auvergne [1] R Aaij et al (LHCb Collaboration), Phys Lett B 699, 330 (2011) week ending 18 NOVEMBER 2011 [2] R Fleischer, N Serra, 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K Carvalho Akiba,23 G Casse,48 M Cattaneo,37 M Charles,51 Ph Charpentier,37 N Chiapolini,39 X Cid Vidal,36 P E L Clarke,46 M Clemencic,37 H V Cliff,43 J Closier,37 C Coca,28 V Coco,23 J Cogan,6 P Collins,37 F Constantin,28 G Conti,38a A Contu,51 A Cook,42 M Coombes,42 G Corti,37 G A Cowan,38a R Currie,46 B D’Almagne,7 C D’Ambrosio,37 P David,8 P N Y David,23 I De Bonis,4 S De Capua,21a,21b M De Cian,39 F De Lorenzi,12 J M De Miranda,1 L De Paula,2 P De Simone,18a D Decamp,4 M Deckenhoff,9 H Degaudenzi,38a,37 M Deissenroth,11 L Del Buono,8 C Deplano,15a O Deschamps,5 F Dettori,15a,15b J Dickens,43 H Dijkstra,37 P Diniz Batista,1 D Dossett,44 A Dovbnya,40 F Dupertuis,38a R Dzhelyadin,34 C Eames,49 S Easo,45 U Egede,49 V Egorychev,30 S Eidelman,33 D van Eijk,23 F Eisele,11 S Eisenhardt,46 R Ekelhof,9 L Eklund,47 Ch Elsasser,39 D G d’Enterria,35a,35c D Esperante Pereira,36 L Este`ve,43 A Falabella,16a,16b E Fanchini,20a,20b C Faărber,11 G Fardell,46 C Farinelli,23 S Farry,12 V Fave,38a V Fernandez Albor,36 M Ferro-Luzzi,37 S Filippov,32 C Fitzpatrick,46 M Fontana,10a F Fontanelli,19a,19b R Forty,37 M Frank,37 C Frei,37 M Frosini,17a,17b,37 S Furcas,20a A Gallas Torreira,36 D Galli,14a,14b M Gandelman,2 P Gandini,51 Y Gao,3 J-C Garnier,37 J Garofoli,52 L Garrido,35a C Gaspar,37 N Gauvin,38a M Gersabeck,37 T Gershon,44 Ph Ghez,4 V Gibson,43 V V Gligorov,37 C Goăbel,54 D Golubkov,30 A Golutvin,49,30,37 A Gomes,2 H Gordon,51 M Grabalosa Ga´ndara,35a R Graciani Diaz,35a L A Granado Cardoso,37 E Grauge´s,35a G Graziani,17a A Grecu,28 S Gregson,43 B Gui,52 E Gushchin,32 Yu Guz,34 T Gys,37 G Haefeli,38a S C Haines,43 T Hampson,42 S Hansmann-Menzemer,11 R Harji,49 N Harnew,51 J Harrison,50 P F Harrison,44 J He,7 V Heijne,23 K Hennessy,48 P Henrard,5 J A Hernando Morata,36 E van Herwijnen,37 W Hofmann,10a K Holubyev,11 P Hopchev,4 W Hulsbergen,23 P Hunt,51 T Huse,48 R S Huston,12 D Hutchcroft,48 D Hynds,47 V Iakovenko,41 P Ilten,12 J Imong,42 R Jacobsson,37 M Jahjah Hussein,5 E Jans,23 F Jansen,23 P Jaton,38a B Jean-Marie,7 F Jing,3 M John,51 211801-5 PHYSICAL REVIEW LETTERS PRL 107, 211801 (2011) week ending 18 NOVEMBER 2011 D Johnson,51 C R Jones,43 B Jost,37 S Kandybei,40 T M Karbach,9 J Keaveney,12 U Kerzel,37 T Ketel,24 A Keune,38a B Khanji,6 Y M Kim,46 M Knecht,38a S Koblitz,37 P Koppenburg,23 A Kozlinskiy,23 L Kravchuk,32 K Kreplin,11 G Krocker,11 P Krokovny,11 F Kruse,9 K Kruzelecki,37 M Kucharczyk,20a,25 S Kukulak,25 R Kumar,14a,37 T Kvaratskheliya,30,37 V N La Thi,38a D Lacarrere,37 G Lafferty,50 A Lai,15a D Lambert,46 R W Lambert,37 E Lanciotti,37 G Lanfranchi,18a C Langenbruch,11 T Latham,44 R Le Gac,6 J van Leerdam,23 J.-P Lees,4 R Lefe`vre,5 A Leflat,31,37 J Lefranc¸ois,7 O Leroy,6 T Lesiak,25 L Li,3 Y Y Li,43 L Li Gioi,5 M Lieng,9 R Lindner,37 C Linn,11 B Liu,3 G Liu,37 J H Lopes,2 E Lopez Asamar,35a N Lopez-March,38a J Luisier,38a F Machefert,7 I V Machikhiliyan,4,30 F Maciuc,10a O Maev,29,37 J Magnin,1 A Maier,37 S Malde,51 R M D Mamunur,37 G Manca,15a,15b G Mancinelli,6 N Mangiafave,43 U Marconi,14a R Maărki,38a J Marks,11 G Martellotti,22a A Martens,7 L Martin,51 A Martı´n Sa´nchez,7 D Martinez Santos,37 A Massafferri,1 Z Mathe,12 C Matteuzzi,20a M Matveev,29 E Maurice,6 B Maynard,52 A Mazurov,32,16a,37 G McGregor,50 R McNulty,12 C Mclean,14a M Meissner,11 M Merk,23 J Merkel,9 R Messi,21a,21b S Miglioranzi,37 D A Milanes,13a,37 M.-N Minard,4 S Monteil,5 D Moran,12 P Morawski,25 J V Morris,45 R Mountain,52 I Mous,23 F Muheim,46 K Muăller,39 R Muresan,28,38a B Muryn,26 M Musy,35a P Naik,42 T Nakada,38a R Nandakumar,45 J Nardulli,45 M Nedos,9 M Needham,46 N Neufeld,37 C Nguyen-Mau,38a,38b M Nicol,7 S Nies,9 V Niess,5 N Nikitin,31 A Oblakowska-Mucha,26 V Obraztsov,34 S Oggero,23 S Ogilvy,47 O Okhrimenko,41 R Oldeman,15a,15b M Orlandea,28 J M Otalora Goicochea,2 B Pal,52 J Palacios,39 M Palutan,18a J Panman,37 A Papanestis,45 M Pappagallo,13a,13b C Parkes,47,37 C J Parkinson,49 G Passaleva,17a G D Patel,48 M Patel,49 S K Paterson,49 G N Patrick,45 C Patrignani,19a,19b C Pavel-Nicorescu,28 A Pazos Alvarez,36 A Pellegrino,23 G Penso,22a,22b M Pepe Altarelli,37 S Perazzini,14a,14b D L Perego,20a,20b E Perez Trigo,36 A Pe´rez-Calero Yzquierdo,35a P Perret,5 M Perrin-Terrin,6 G Pessina,20a A Petrella,16a,37 A Petrolini,19a,19b B Pie Valls,35a B Pietrzyk,4 T Pilar,44 D Pinci,22a R Plackett,47 S Playfer,46 M Plo Casasus,36 G Polok,25 A Poluektov,44,33 E Polycarpo,2 D Popov,10a B Popovici,28 C Potterat,35a A Powell,51 T du Pree,23 V Pugatch,41 A Puig Navarro,35a W Qian,52 J H Rademacker,42 B Rakotomiaramanana,38a I Raniuk,40 G Raven,24 S Redford,51 M M Reid,44 A C dos Reis,1 S Ricciardi,45 K Rinnert,48 D A Roa Romero,5 P Robbe,7 E Rodrigues,47 F Rodrigues,2 C Rodriguez Cobo,36 P Rodriguez Perez,36 G J Rogers,43 V Romanovsky,34 J Rouvinet,38a T Ruf,37 H Ruiz,35a G Sabatino,21a,21b J J Saborido Silva,36 N Sagidova,29 P Sail,47 B Saitta,15a,15b C Salzmann,39 M Sannino,19a,19b R Santacesaria,22a R Santinelli,37 E Santovetti,21a,21b M Sapunov,6 A Sarti,18a,18b C Satriano,22a,22c A Satta,21a M Savrie,16a,16b D Savrina,30 P Schaack,49 M Schiller,11 S Schleich,9 M Schmelling,10a B Schmidt,37 O Schneider,38a A Schopper,37 M.-H Schune,7 R Schwemmer,37 A Sciubba,18a,18b M Seco,36 A Semennikov,30 K Senderowska,26 N Serra,39 J Serrano,6 P Seyfert,11 B Shao,3 M Shapkin,34 I Shapoval,40,37 P Shatalov,30 Y Shcheglov,29 T Shears,48 L Shekhtman,33 O Shevchenko,40 V Shevchenko,30 A Shires,49 R Silva Coutinho,54 H P Skottowe,43 T Skwarnicki,52 A C Smith,37 N A Smith,48 K Sobczak,5 F J P Soler,47 A Solomin,42 F Soomro,49 B Souza De Paula,2 B Spaan,9 A Sparkes,46 P Spradlin,47 F Stagni,37 S Stahl,11 O Steinkamp,39 S Stoica,28 S Stone,52,37 B Storaci,23 U Straumann,39 N Styles,46 S Swientek,9 M Szczekowski,27 P Szczypka,38a T Szumlak,26 S T’Jampens,4 E Teodorescu,28 F Teubert,37 C Thomas,51,45 E Thomas,37 J van Tilburg,11 V Tisserand,4 M Tobin,39 S Topp-Joergensen,51 M T Tran,38a A Tsaregorodtsev,6 N Tuning,23 A Ukleja,27 P Urquijo,52 U Uwer,11 V Vagnoni,14a G Valenti,14a R Vazquez Gomez,35a P Vazquez Regueiro,36 S Vecchi,16a J J Velthuis,42 M Veltri,17a,17c K Vervink,37 B Viaud,7 I Videau,7 X Vilasis-Cardona,35a,35b J Visniakov,36 A Vollhardt,39 D Voong,42 A Vorobyev,29 H Voss,10a K Wacker,9 S Wandernoth,11 J Wang,52 D R Ward,43 A D Webber,50 D Websdale,49 M Whitehead,44 D Wiedner,11 L Wiggers,23 G Wilkinson,51 M P Williams,44,45 M Williams,49 F F Wilson,45 J Wishahi,9 M Witek,25 W Witzeling,37 S A Wotton,43 K Wyllie,37 Y Xie,46 F Xing,51 Z Yang,3 R Young,46 O Yushchenko,34 M Zavertyaev,10a,10b L Zhang,52 W C Zhang,12 Y Zhang,3 A Zhelezov,11 L Zhong,3 E Zverev,31 and A Zvyagin37 (LHCb Collaboration) Centro Brasileiro de Pesquisas Fı´sicas (CBPF), Rio de Janeiro, Brazil Universidade Federal Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil Center for High Energy Physics, Tsinghua University, Beijing, China LAPP, Universite´ de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France Clermont Universite´, Universite´ Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France 211801-6 PHYSICAL REVIEW LETTERS PRL 107, 211801 (2011) week ending 18 NOVEMBER 2011 CPPM, Aix-Marseille Universite´, CNRS/IN2P3, Marseille, France LAL, Universite´ Paris-Sud, CNRS/IN2P3, Orsay, France LPNHE, Universite´ Pierre et Marie Curie, Universite´ Paris Diderot, CNRS/IN2P3, Paris, France Fakultaăt Physik, Technische Universitaăt Dortmund, Dortmund, Germany 10a Max-Planck-Institut fuăr Kernphysik (MPIK), Heidelberg, Germany 10b P N Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia 11 Physikalisches Institut, Ruprecht-Karls-Universitaăt Heidelberg, Heidelberg, Germany 12 School of Physics, University College Dublin, Dublin, Ireland 13a Sezione INFN di Bari, Bari, Italy 13b Universita` di Bari, Bari, Italy 14a Sezione INFN di Bologna, Bologna, Italy 14b Universita` di Bologna, Bologna, Italy 15a Sezione INFN di Cagliari, Cagliari, Italy 15b Universita` di Cagliari, Cagliari, Italy 16a Sezione INFN di Ferrara, Ferrara, Italy 16b Universita` di Ferrara, Ferrara, Italy 17a Sezione INFN di Firenze, Firenze, Italy 17b Universita` di Firenze, Firenze, Italy 17c Universita` di Urbino, Urbino, Italy 17d Universita` di Modena e Reggio Emilia, Modena, Italy 18a Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy 18b Universita` di Roma La Sapienza, Roma, Italy 19a Sezione INFN di Genova, Genova, Italy 19b Universita` di Genova, Genova, Italy 20a Sezione INFN di Milano Bicocca, Milano, Italy 20b Universita` di Milano Bicocca, Milano, Italy 21a Sezione INFN di Roma Tor Vergata, Roma, Italy 21b Universita` di Roma Tor Vergata, Roma, Italy 22a Sezione INFN di Roma La Sapienza, Roma, Italy 22b Universita` di Roma La Sapienza, Roma, Italy 22c Universita` della Basilicata, Potenza, Italy 23 Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands 24 Nikhef National Institute for Subatomic Physics and Vrije Universiteit, Amsterdam, The Netherlands 25 Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Cracow, Poland 26 Faculty of Physics and Applied Computer Science, Cracow, Poland 27 Soltan Institute for Nuclear Studies, Warsaw, Poland 28 Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania 29 Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia 30 Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia 31 Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia 32 Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia 33 Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia 34 Institute for High Energy Physics (IHEP), Protvino, Russia 35a Universitat de Barcelona, Barcelona, Spain 35b LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain 35c Institucio´ Catalana de Recerca i Estudis Avanc¸ats (ICREA), Barcelona, Spain 36 Universidad de Santiago de Compostela, Santiago de Compostela, Spain 37 European Organization for Nuclear Research (CERN), Geneva, Switzerland 38a Ecole Polytechnique Fe´de´rale de Lausanne (EPFL), Lausanne, Switzerland 38b Hanoi University of Science, Hanoi, Vietnam 39 Physik-Institut, Universitaăt Zuărich, Zuărich, Switzerland 40 NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine 41 Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine 42 H H Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom 43 Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom 44 Department of Physics, University of Warwick, Coventry, United Kingdom 45 STFC Rutherford Appleton Laboratory, Didcot, United Kingdom 46 School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom 47 School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 48 Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 49 Imperial College London, London, United Kingdom 211801-7 PRL 107, 211801 (2011) PHYSICAL REVIEW LETTERS 50 week ending 18 NOVEMBER 2011 School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 51 Department of Physics, University of Oxford, Oxford, United Kingdom 52 Syracuse University, Syracuse, New York, USA 53 CC-IN2P3, CNRS/IN2P3, Lyon-Villeurbanne, France* 54 Pontifı´cia Universidade Cato´lica Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil† *Associated member † Associated to Universidade Federal Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil 211801-8 ... efficiency The dominant source of systematic uncertainty is the knowledge of the B0 ! D ỵ branching fraction (for the B0 ! D Kỵ branching fraction measurement) and the knowledge of the DÀ and DÀ s branching. .. 0:017stat ặ 0:017syst ặ 0:020theor : (7) In summary, with 35 pbÀ1 of data collected by using the LHCb detector during the 2010 LHC operation at a centerof-mass energy of TeV, the branching fraction. .. method from the data to simulated events, and the maximum discrepancy found between the calibration method and the true misidentification is attributed as a systematic uncertainty The fs =fd measurement